Represent the complex number $z=1+i \sqrt{3}$ in the polar form.

(N/A) Let $1=r \cos \theta$ and $\sqrt{3}=r \sin \theta$.
By squaring and adding,we get:
$r^{2}(\cos ^{2} \theta+\sin ^{2} \theta)=1^{2}+(\sqrt{3})^{2}$
$r^{2}(1)=1+3=4$
$r=\sqrt{4}=2$ (conventionally,$r>0$).
Therefore,$\cos \theta=\frac{1}{2}$ and $\sin \theta=\frac{\sqrt{3}}{2}$,which gives $\theta=\frac{\pi}{3}$.
Thus,the required polar form is $z=2(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3})$.
The complex number $z=1+i \sqrt{3}$ is represented in the Cartesian plane as shown in the figure.